On cardinal sequences of Boolean algebras
✍ Scribed by Martin Weese
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 609 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0002-5240
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📜 SIMILAR VOLUMES
Lct 1 be an infinite cardinal and let A , B be Boolean algebras. A homomorphism h: , 4 4 B is said to be A-cmpkte if whenever X is a subset of A of cardinality I such that the join V X of X exists in A , then V h[X] exists in B and is equal to h(V X ) . If x is an infinite cardinal, B is said to be
We prove that if GCH holds and τ = κα : α < η is a sequence of infinite cardinals such that κα ≥ |η| for each α < η, then there is a cardinal-preserving partial order that forces the existence of a scattered Boolean space whose cardinal sequence is τ .
## Abstract For an infinite cardinal __K__ a stronger version of __K__‐distributivity for Boolean algebras, called k‐partition completeness, is defined and investigated (e. g. every __K__‐Suslin algebra is a __K__‐partition complete Boolean algebra). It is shown that every __k__‐partition complete
It was proved by Dow and Simon that there are 2"' (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height WI and width w. In this paper, we prove that if cy is an ordinal with WI < 01 < w2 and 19 = (KC: [ < cx) is a sequence of cardinals such that either KC = w or KC =